/*
 * Copyright Takuya OOURA, 1996-2001
 *
 * You may use, copy, modify and distribute this code
 * for any purpose (include commercial use) and without fee.
 * Please refer to this package when you modify this code.
 */
package com.audio.util.ssrc;

/**
 * Fast Fourier/Cosine/Sine Transform.
 * <pre>
 *  dimension   :one
 *  data length :power of 2
 *  decimation  :frequency
 *  radix       :<b>split-radix</b>
 *  data        :inplace
 *  table       :use
 * </pre>
 * <h4>Appendix:</h4>
 * <p>
 * The cos/sin table is recalculated when the larger table required.
 * w[] and ip[] are compatible with all routines.
 * </p>
 *
 * @author <a href="mailto:ooura@mmm.t.u-tokyo.ac.jp">Takuya OOURA</a>
 * @author <a href="mailto:vavivavi@yahoo.co.jp">Naohide Sano</a> (nsano)
 * @version 0.00 060127 nsano port to java version <br>
 */
public class SplitRadixFft {

  /** */
  private static final int CDFT_RECURSIVE_N = 512;

  /**
   * Complex Discrete Fourier Transform.
   * <pre>
   *  [definition]
   *      &lt;case1&gt;
   *          X[k] = sum_j=0&amp;circ;n-1 x[j]*exp(2*pi*i*j*k/n), 0&lt;=k&lt;n
   *      &lt;case2&gt;
   *          X[k] = sum_j=0&amp;circ;n-1 x[j]*exp(-2*pi*i*j*k/n), 0&lt;=k&lt;n
   *      (notes: sum_j=0&amp;circ;n-1 is a summation from j=0 to n-1)
   *  [usage]
   *      &lt;case1&gt;
   *          ip[0] = 0; // first time only
   *          cdft(2*n, 1, a, ip, w);
   *      &lt;case2&gt;
   *          ip[0] = 0; // first time only
   *          cdft(2*n, -1, a, ip, w);
   *  [remark]
   *      Inverse of
   *          cdft(2*n, -1, a, ip, w);
   *      is
   *          cdft(2*n, 1, a, ip, w);
   *          for (j = 0; j &lt;= 2 * n - 1; j++) {
   *              a[j] *= 1.0 / n;
   *          }
   *      .
   * </pre>
   *
   * @param n 2*n data length (int)
   * n &gt;= 1, n = power of 2
   * @param a a[0...2*n-1] input/output data (REAL *)
   * input data
   * a[2*j] = Re(x[j]),
   * a[2*j+1] = Im(x[j]), 0&lt;=j&lt;n
   * output data
   * a[2*k] = Re(X[k]),
   * a[2*k+1] = Im(X[k]), 0&lt;=k&lt;n
   * @param ip ip[0...*] work area for bit reversal (int *)
   * length of ip &gt;= 2+sqrt(n)
   * strictly,
   * length of ip &gt;=
   * 2+(1&lt;&lt;(int)(log(n+0.5)/log(2))/2).
   * ip[0],ip[1] are pointers of the cos/sin table.
   * @param w w[0...n/2-1] cos/sin table (REAL *)
   * w[],ip[] are initialized if ip[0] == 0.
   */
  public void cdft(int n, int isgn, double[] a, int[] ip, double[] w) {
    int nw;

    nw = ip[0];
    if (n > (nw << 2)) {
      nw = n >> 2;
      makewt(nw, ip, w);
    }
    if (isgn >= 0) {
      cftfsub(n, a, ip, 2, nw, w);
    } else {
      cftbsub(n, a, ip, 2, nw, w);
    }
  }

  /**
   * Real Discrete Fourier Transform.
   * <pre>
   *  [definition]
   *      &lt;case1&gt; RDFT
   *          R[k] = sum_j = 0 &amp; &circ; (n - 1) a[j] * cos(2 * pi * j * k / n), 0 &lt;= k &lt;=
   * n / 2
   *          I[k] = sum_j = 0 &amp; &circ; (n - 1) a[j] * sin(2 * pi * j * k / n), 0 &lt; k &lt; n
   * / 2
   *      &lt;case2&gt; IRDFT (excluding scaleView)
   *          a[k] = (R[0] + R[n / 2] * cos(pi * k)) / 2 +
   *              sum_j = 1 &amp; &circ; (n / 2 - 1) R[j] * cos(2 * pi * j * k / n) +
   *              sum_j = 1 &amp; &circ; (n / 2 - 1) I[j] * sin(2 * pi * j * k / n), 0 &lt;= k &lt;
   * n
   *  [usage]
   *      &lt;case1&gt;
   *          ip[0] = 0; // first time only
   *          rdft(n, 1, a, ip, w);
   *      &lt;case2&gt;
   *          ip[0] = 0; // first time only
   *          rdft(n, -1, a, ip, w);
   *  [remark]
   *      Inverse of
   *          rdft(n, 1, a, ip, w);
   *      is
   *          rdft(n, -1, a, ip, w);
   *          for (j = 0; j &lt;= n - 1; j++) {
   *              a[j] *= 2.0 / n;
   *          }
   *      .
   * </pre>
   *
   * @param n data length <br>
   * n &gt;= 2, n = power of 2
   * @param a [0...n-1] input/output data
   * <pre>
   *  &lt;case1&gt;
   *      output data
   *          a[2 * k] = R[k], 0 &lt;= k &lt; n / 2
   *          a[2 * k + 1] = I[k], 0 &lt; k &lt; n / 2
   *          a[1] = R[n/2]
   *  &lt;case2&gt;
   *      input data
   *          a[2 * j] = R[j], 0 &lt;= j &lt; n / 2
   *          a[2 * j + 1] = I[j], 0 &lt; j &lt; n / 2
   *          a[1] = R[n / 2]
   * </pre>
   * @param ip [0...*] work area for bit reversal
   * <pre>
   *  length of ip &gt;= 2 + sqrt(n / 2)
   *  strictly,
   *  length of ip &gt;=
   *      2 + (1 &lt;&lt; (int) (log(n / 2 + 0.5) / log(2)) / 2).
   * </pre>
   * ip[0],ip[1] are pointers of the cos/sin table.
   * @param w [0...n/2-1] cos/sin table <br>
   * w[],ip[] are initialized if ip[0] == 0.
   */
  public void rdft(int n, int isgn, double[] a, int[] ip, double[] w) {
    int nw, nc;
    double xi;

    nw = ip[0];
    if (n > (nw << 2)) {
      nw = n >> 2;
      makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > (nc << 2)) {
      nc = n >> 2;
      makect(nc, ip, w, nw);
    }
    if (isgn >= 0) {
      if (n > 4) {
        cftfsub(n, a, ip, 2, nw, w);
        rftfsub(n, a, nc, w, nw);
      } else if (n == 4) {
        cftfsub(n, a, ip, 2, nw, w);
      }
      xi = a[0] - a[1];
      a[0] += a[1];
      a[1] = xi;
    } else {
      a[1] = 0.5 * (a[0] - a[1]);
      a[0] -= a[1];
      if (n > 4) {
        rftbsub(n, a, nc, w, nw);
        cftbsub(n, a, ip, 2, nw, w);
      } else if (n == 4) {
        cftbsub(n, a, ip, 2, nw, w);
      }
    }
  }

  /**
   * Discrete Cosine Transform.
   * <pre>
   *  [definition]
   *      &lt;case1&gt; IDCT (excluding scaleView)
   *          C[k] = sum_j=0&amp;circ;n-1 a[j]*cos(pi*j*(k+1/2)/n), 0&lt;=k&lt;n
   *      &lt;case2&gt; DCT
   *          C[k] = sum_j=0&amp;circ;n-1 a[j]*cos(pi*(j+1/2)*k/n), 0&lt;=k&lt;n
   *  [usage]
   *      &lt;case1&gt;
   *          ip[0] = 0; // first time only
   *          ddct(n, 1, a, ip, w);
   *      &lt;case2&gt;
   *          ip[0] = 0; // first time only
   *          ddct(n, -1, a, ip, w);
   *  [remark]
   *      Inverse of
   *          ddct(n, -1, a, ip, w);
   *      is
   *          a[0] *= 0.5;
   *          ddct(n, 1, a, ip, w);
   *          for (j = 0; j &lt;= n - 1; j++) {
   *              a[j] *= 2.0 / n;
   *          }
   *      .
   * </pre>
   *
   * @param n data length (int)
   * <pre>
   *  n &gt;= 2, n = power of 2
   * </pre>
   * @param a [0...n-1] input/output data (REAL *)
   * <pre>
   *  output data
   *      a[k] = C[k], 0&lt;=k&lt;n
   * </pre>
   * @param ip [0...*] work area for bit reversal (int *)
   * <pre>
   *  length of ip &gt;= 2+sqrt(n/2)
   *  strictly,
   *  length of ip &gt;=
   *      2+(1&lt;&lt;(int)(log(n/2+0.5)/log(2))/2).
   *  ip[0],ip[1] are pointers of the cos/sin table.
   * </pre>
   * @param w [0...n*5/4-1] cos/sin table (REAL *)
   * <pre>
   *  w[],ip[] are initialized if ip[0] == 0.
   * </pre>
   */
  public void ddct(int n, int isgn, double[] a, int[] ip, double[] w) {
    int j, nw, nc;
    double xr;

    nw = ip[0];
    if (n > (nw << 2)) {
      nw = n >> 2;
      makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > nc) {
      nc = n;
      makect(nc, ip, w, nw);
    }
    if (isgn < 0) {
      xr = a[n - 1];
      for (j = n - 2; j >= 2; j -= 2) {
        a[j + 1] = a[j] - a[j - 1];
        a[j] += a[j - 1];
      }
      a[1] = a[0] - xr;
      a[0] += xr;
      if (n > 4) {
        rftbsub(n, a, nc, w, nw);
        cftbsub(n, a, ip, 2, nw, w);
      } else if (n == 4) {
        cftbsub(n, a, ip, 2, nw, w);
      }
    }
    dctsub(n, a, nc, w, nw);
    if (isgn >= 0) {
      if (n > 4) {
        cftfsub(n, a, ip, 2, nw, w);
        rftfsub(n, a, nc, w, nw);
      } else if (n == 4) {
        cftfsub(n, a, ip, 2, nw, w);
      }
      xr = a[0] - a[1];
      a[0] += a[1];
      for (j = 2; j < n; j += 2) {
        a[j - 1] = a[j] - a[j + 1];
        a[j] += a[j + 1];
      }
      a[n - 1] = xr;
    }
  }

  /**
   * Discrete Sine Transform.
   * <pre>
   *  [definition]
   *      &lt;case1&gt; IDST (excluding scaleView)
   *          S[k] = sum_j=1&circ;n A[j]*sin(pi*j*(k+1/2)/n), 0&lt;=k&lt;n
   *      &lt;case2&gt; DST
   *          S[k] = sum_j=0&circ;n-1 a[j]*sin(pi*(j+1/2)*k/n), 0&lt;k&lt;=n
   *  [usage]
   *      &lt;case1&gt;
   *          ip[0] = 0; // first time only
   *          ddst(n, 1, a, ip, w);
   *      &lt;case2&gt;
   *          ip[0] = 0; // first time only
   *          ddst(n, -1, a, ip, w);
   *  [remark]
   *      Inverse of
   *          ddst(n, -1, a, ip, w);
   *      is
   *          a[0] *= 0.5;
   *          ddst(n, 1, a, ip, w);
   *          for (j = 0; j &lt;= n - 1; j++) {
   *              a[j] *= 2.0 / n;
   *          }
   *      .
   * </pre>
   *
   * @param n data length (int)
   * n &gt;= 2, n = power of 2
   * @param a [0...n-1] input/output data (REAL *)
   * &lt;case1&gt;
   * input data
   * a[j] = A[j], 0&lt;j&lt;n
   * a[0] = A[n]
   * output data
   * a[k] = S[k], 0&lt;=k&lt;n
   * &lt;case2&gt;
   * output data
   * a[k] = S[k], 0&lt;k&lt;n
   * a[0] = S[n]
   * @param ip [0...*] work area for bit reversal (int *)
   * length of ip &gt;= 2+sqrt(n/2)
   * strictly,
   * length of ip &gt;=
   * 2+(1&lt;&lt;(int)(log(n/2+0.5)/log(2))/2).
   * ip[0],ip[1] are pointers of the cos/sin table.
   * @param w [0...n*5/4-1] cos/sin table (REAL *)
   * w[],ip[] are initialized if ip[0] == 0.
   */
  public void ddst(int n, int isgn, double[] a, int[] ip, double[] w) {
    int j, nw, nc;
    double xr;

    nw = ip[0];
    if (n > (nw << 2)) {
      nw = n >> 2;
      makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > nc) {
      nc = n;
      makect(nc, ip, w, nw);
    }
    if (isgn < 0) {
      xr = a[n - 1];
      for (j = n - 2; j >= 2; j -= 2) {
        a[j + 1] = -a[j] - a[j - 1];
        a[j] -= a[j - 1];
      }
      a[1] = a[0] + xr;
      a[0] -= xr;
      if (n > 4) {
        rftbsub(n, a, nc, w, nw);
        cftbsub(n, a, ip, 2, nw, w);
      } else if (n == 4) {
        cftbsub(n, a, ip, 2, nw, w);
      }
    }
    dstsub(n, a, nc, w, nw);
    if (isgn >= 0) {
      if (n > 4) {
        cftfsub(n, a, ip, 2, nw, w);
        rftfsub(n, a, nc, w, nw);
      } else if (n == 4) {
        cftfsub(n, a, ip, 2, nw, w);
      }
      xr = a[0] - a[1];
      a[0] += a[1];
      for (j = 2; j < n; j += 2) {
        a[j - 1] = -a[j] - a[j + 1];
        a[j] -= a[j + 1];
      }
      a[n - 1] = -xr;
    }
  }

  /**
   * Cosine Transform of RDFT (Real Symmetric DFT).
   * <pre>
   *  [definition]
   *      C[k] = sum_j=0&circ;n a[j]*cos(pi*j*k/n), 0&lt;=k&lt;=n
   *  [usage]
   *      ip[0] = 0; // first time only
   *      dfct(n, a, t, ip, w);
   *  [parameters]
   *  [remark]
   *      Inverse of
   *          a[0] *= 0.5;
   *          a[n] *= 0.5;
   *          dfct(n, a, t, ip, w);
   *      is
   *          a[0] *= 0.5;
   *          a[n] *= 0.5;
   *          dfct(n, a, t, ip, w);
   *          for (j = 0; j &lt;= n; j++) {
   *              a[j] *= 2.0 / n;
   *          }
   *      .
   * </pre>
   *
   * @param n data length - 1 (int)
   * <pre>
   *  n &gt;= 2, n = power of 2
   * </pre>
   * @param a [0...n] input/output data (REAL *)
   * <pre>
   *  output data
   *      a[k] = C[k], 0&lt;=k&lt;=n
   * </pre>
   * @param t [0...n/2] work area (REAL *)
   * @param ip [0...*] work area for bit reversal (int *)
   * <pre>
   *  length of ip &gt;= 2+sqrt(n/4)
   *  strictly,
   *  length of ip &gt;=
   *      2+(1&lt;&lt;(int)(log(n/4+0.5)/log(2))/2).
   *  ip[0],ip[1] are pointers of the cos/sin table.
   * </pre>
   * @param w [0...n*5/8-1] cos/sin table (REAL *)
   * <pre>
   *  w[],ip[] are initialized if ip[0] == 0.
   * </pre>
   */
  public void dfct(int n, double[] a, double[] t, int[] ip, double[] w) {
    int j, k, l, m, mh, nw, nc;
    double xr, xi, yr, yi;

    nw = ip[0];
    if (n > (nw << 3)) {
      nw = n >> 3;
      makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > (nc << 1)) {
      nc = n >> 1;
      makect(nc, ip, w, nw);
    }
    m = n >> 1;
    yi = a[m];
    xi = a[0] + a[n];
    a[0] -= a[n];
    t[0] = xi - yi;
    t[m] = xi + yi;
    if (n > 2) {
      mh = m >> 1;
      for (j = 1; j < mh; j++) {
        k = m - j;
        xr = a[j] - a[n - j];
        xi = a[j] + a[n - j];
        yr = a[k] - a[n - k];
        yi = a[k] + a[n - k];
        a[j] = xr;
        a[k] = yr;
        t[j] = xi - yi;
        t[k] = xi + yi;
      }
      t[mh] = a[mh] + a[n - mh];
      a[mh] -= a[n - mh];
      dctsub(m, a, nc, w, nw);
      if (m > 4) {
        cftfsub(m, a, ip, 2, nw, w);
        rftfsub(m, a, nc, w, nw);
      } else if (m == 4) {
        cftfsub(m, a, ip, 2, nw, w);
      }
      a[n - 1] = a[0] - a[1];
      a[1] = a[0] + a[1];
      for (j = m - 2; j >= 2; j -= 2) {
        a[2 * j + 1] = a[j] + a[j + 1];
        a[2 * j - 1] = a[j] - a[j + 1];
      }
      l = 2;
      m = mh;
      while (m >= 2) {
        dctsub(m, t, nc, w, nw);
        if (m > 4) {
          cftfsub(m, t, ip, 2, nw, w);
          rftfsub(m, t, nc, w, nw);
        } else if (m == 4) {
          cftfsub(m, t, ip, 2, nw, w);
        }
        a[n - l] = t[0] - t[1];
        a[l] = t[0] + t[1];
        k = 0;
        for (j = 2; j < m; j += 2) {
          k += l << 2;
          a[k - l] = t[j] - t[j + 1];
          a[k + l] = t[j] + t[j + 1];
        }
        l <<= 1;
        mh = m >> 1;
        for (j = 0; j < mh; j++) {
          k = m - j;
          t[j] = t[m + k] - t[m + j];
          t[k] = t[m + k] + t[m + j];
        }
        t[mh] = t[m + mh];
        m = mh;
      }
      a[l] = t[0];
      a[n] = t[2] - t[1];
      a[0] = t[2] + t[1];
    } else {
      a[1] = a[0];
      a[2] = t[0];
      a[0] = t[1];
    }
  }

  /**
   * Sine Transform of RDFT (Real Anti-symmetric DFT).
   * <pre>
   *  [definition]
   *      S[k] = sum_j=1&amp;circ;n-1 a[j]*sin(pi*j*k/n), 0&lt;k&lt;n
   *  [usage]
   *      ip[0] = 0; // first time only
   *      dfst(n, a, t, ip, w);
   *  [remark]
   *      Inverse of
   *          dfst(n, a, t, ip, w);
   *      is
   *          dfst(n, a, t, ip, w);
   *          for (j = 1; j &lt;= n - 1; j++) {
   *              a[j] *= 2.0 / n;
   *          }
   *      .
   * </pre>
   *
   * @param n data length + 1 (int)
   * <pre>
   *  n &gt;= 2, n = power of 2
   * </pre>
   * @param a [0...n-1] input/output data (REAL *)
   * <pre>
   *  output data
   *      a[k] = S[k], 0&lt;k&lt;n
   *      (a[0] is used for work area)
   * </pre>
   * @param t [0...n/2-1] work area (REAL *)
   * @param ip [0...*] work area for bit reversal (int *)
   * <pre>
   *  length of ip &gt;= 2+sqrt(n/4)
   *  strictly,
   *  length of ip &gt;=
   *      2+(1&lt;&lt;(int)(log(n/4+0.5)/log(2))/2).
   *  ip[0],ip[1] are pointers of the cos/sin table.
   * </pre>
   * @param w [0...n*5/8-1] cos/sin table (REAL *)
   * <pre>
   *  w[],ip[] are initialized if ip[0] == 0.
   * </pre>
   */
  public void dfst(int n, double[] a, double[] t, int[] ip, double[] w) {
    int j, k, l, m, mh, nw, nc;
    double xr, xi, yr, yi;

    nw = ip[0];
    if (n > (nw << 3)) {
      nw = n >> 3;
      makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > (nc << 1)) {
      nc = n >> 1;
      makect(nc, ip, w, nw);
    }
    if (n > 2) {
      m = n >> 1;
      mh = m >> 1;
      for (j = 1; j < mh; j++) {
        k = m - j;
        xr = a[j] + a[n - j];
        xi = a[j] - a[n - j];
        yr = a[k] + a[n - k];
        yi = a[k] - a[n - k];
        a[j] = xr;
        a[k] = yr;
        t[j] = xi + yi;
        t[k] = xi - yi;
      }
      t[0] = a[mh] - a[n - mh];
      a[mh] += a[n - mh];
      a[0] = a[m];
      dstsub(m, a, nc, w, nw);
      if (m > 4) {
        cftfsub(m, a, ip, 2, nw, w);
        rftfsub(m, a, nc, w, nw);
      } else if (m == 4) {
        cftfsub(m, a, ip, 2, nw, w);
      }
      a[n - 1] = a[1] - a[0];
      a[1] = a[0] + a[1];
      for (j = m - 2; j >= 2; j -= 2) {
        a[2 * j + 1] = a[j] - a[j + 1];
        a[2 * j - 1] = -a[j] - a[j + 1];
      }
      l = 2;
      m = mh;
      while (m >= 2) {
        dstsub(m, t, nc, w, nw);
        if (m > 4) {
          cftfsub(m, t, ip, 2, nw, w);
          rftfsub(m, t, nc, w, nw);
        } else if (m == 4) {
          cftfsub(m, t, ip, 2, nw, w);
        }
        a[n - l] = t[1] - t[0];
        a[l] = t[0] + t[1];
        k = 0;
        for (j = 2; j < m; j += 2) {
          k += l << 2;
          a[k - l] = -t[j] - t[j + 1];
          a[k + l] = t[j] - t[j + 1];
        }
        l <<= 1;
        mh = m >> 1;
        for (j = 1; j < mh; j++) {
          k = m - j;
          t[j] = t[m + k] + t[m + j];
          t[k] = t[m + k] - t[m + j];
        }
        t[0] = t[m + mh];
        m = mh;
      }
      a[l] = t[0];
    }
    a[0] = 0;
  }

  // -------- initializing routines --------

  /** */
  private void makewt(int nw, int[] ip, double[] w) {
    int j, nwh, nw0, nw1;
    double delta, wn4r, wk1r, wk1i, wk3r, wk3i;

    ip[0] = nw;
    ip[1] = 1;
    if (nw > 2) {
      nwh = nw >> 1;
      //          delta = Math.atan(1.0) / nwh;
      delta = Math.PI / 4 / nwh;
      wn4r = Math.cos(delta * nwh);
      w[0] = 1;
      w[1] = wn4r;
      if (nwh >= 4) {
        w[2] = 0.5 / Math.cos(delta * 2);
        w[3] = 0.5 / Math.cos(delta * 6);
      }
      for (j = 4; j < nwh; j += 4) {
        w[j] = Math.cos(delta * j);
        w[j + 1] = Math.sin(delta * j);
        w[j + 2] = Math.cos(3 * delta * j);
        w[j + 3] = Math.sin(3 * delta * j);
      }
      nw0 = 0;
      while (nwh > 2) {
        nw1 = nw0 + nwh;
        nwh >>= 1;
        w[nw1] = 1;
        w[nw1 + 1] = wn4r;
        if (nwh >= 4) {
          wk1r = w[nw0 + 4];
          wk3r = w[nw0 + 6];
          w[nw1 + 2] = 0.5 / wk1r;
          w[nw1 + 3] = 0.5 / wk3r;
        }
        for (j = 4; j < nwh; j += 4) {
          wk1r = w[nw0 + 2 * j];
          wk1i = w[nw0 + 2 * j + 1];
          wk3r = w[nw0 + 2 * j + 2];
          wk3i = w[nw0 + 2 * j + 3];
          w[nw1 + j] = wk1r;
          w[nw1 + j + 1] = wk1i;
          w[nw1 + j + 2] = wk3r;
          w[nw1 + j + 3] = wk3i;
        }
        nw0 = nw1;
      }
    }
  }

  /** */
  private void makect(int nc, int[] ip, double[] c, int cP) {
    int j, nch;
    double delta;

    ip[1] = nc;
    if (nc > 1) {
      nch = nc >> 1;
      //          delta = Math.atan(1.0) / nch;
      delta = Math.PI / 4 / nch;
      c[cP + 0] = Math.cos(delta * nch);
      c[cP + nch] = 0.5 * c[cP + 0];
      for (j = 1; j < nch; j++) {
        c[cP + j] = 0.5 * Math.cos(delta * j);
        c[cP + nc - j] = 0.5 * Math.sin(delta * j);
      }
    }
  }

  // -------- child routines --------

  /**
   * 2nd
   *
   * @see #rdft(int, int, double[], int[], double[])
   * @see #ddct(int, int, double[], int[], double[])
   * @see #cdft(int, int, double[], int[], double[])
   * @see #ddst(int, int, double[], int[], double[])
   * @see #dfst(int, double[], double[], int[], double[])
   * @see #dfct(int, double[], double[], int[], double[])
   */
  private void cftfsub(int n, double[] a, int[] ip, int ipP, int nw, double[] w) {
    int m;

    if (n > 32) {
      m = n >> 2;
      cftf1st(n, a, w, nw - m);
      if (n > CDFT_RECURSIVE_N) {
        cftrec1(m, a, 0, nw, w);
        cftrec2(m, a, m, nw, w);
        cftrec1(m, a, 2 * m, nw, w);
        cftrec1(m, a, 3 * m, nw, w);
      } else if (m > 32) {
        cftexp1(n, a, 0, nw, w);
      } else {
        cftfx41(n, a, 0, nw, w);
      }
      bitrv2(n, ip, ipP, a);
    } else if (n > 8) {
      if (n == 32) {
        cftf161(a, 0, w, nw - 8);
        bitrv216(a);
      } else {
        cftf081(a, 0, w, 0);
        bitrv208(a);
      }
    } else if (n == 8) {
      cftf040(a);
    } else if (n == 4) {
      cftx020(a);
    }
  }

  /**
   * 2nd
   *
   * @see #rdft(int, int, double[], int[], double[])
   * @see #ddct(int, int, double[], int[], double[])
   * @see #cdft(int, int, double[], int[], double[])
   * @see #ddst(int, int, double[], int[], double[])
   */
  private void cftbsub(int n, double[] a, int[] ip, int ipP, int nw, double[] w) {
    int m;

    if (n > 32) {
      m = n >> 2;
      cftb1st(n, a, w, nw - m);
      if (n > CDFT_RECURSIVE_N) {
        cftrec1(m, a, 0, nw, w);
        cftrec2(m, a, m, nw, w);
        cftrec1(m, a, 2 * m, nw, w);
        cftrec1(m, a, 3 * m, nw, w);
      } else if (m > 32) {
        cftexp1(n, a, 0, nw, w);
      } else {
        cftfx41(n, a, 0, nw, w);
      }
      bitrv2conj(n, ip, ipP, a);
    } else if (n > 8) {
      if (n == 32) {
        cftf161(a, 0, w, nw - 8);
        bitrv216neg(a);
      } else {
        cftf081(a, 0, w, 0);
        bitrv208neg(a);
      }
    } else if (n == 8) {
      cftb040(a);
    } else if (n == 4) {
      cftx020(a);
    }
  }

  /**
   * 3rd
   *
   * @see #cftfsub(int, double[], int[], int, int, double[])
   */
  private final void bitrv2(int n, int[] ip, int ipP, double[] a) {
    int j, j1, k, k1, l, m, m2;
    double xr, xi, yr, yi;

    ip[ipP + 0] = 0;
    l = n;
    m = 1;
    while ((m << 3) < l) {
      l >>= 1;
      for (j = 0; j < m; j++) {
        ip[ipP + m + j] = ip[ipP + j] + l;
      }
      m <<= 1;
    }
    m2 = 2 * m;
    if ((m << 3) == l) {
      for (k = 0; k < m; k++) {
        for (j = 0; j < k; j++) {
          j1 = 2 * j + ip[ipP + k];
          k1 = 2 * k + ip[ipP + j];
          xr = a[j1];
          xi = a[j1 + 1];
          yr = a[k1];
          yi = a[k1 + 1];
          a[j1] = yr;
          a[j1 + 1] = yi;
          a[k1] = xr;
          a[k1 + 1] = xi;
          j1 += m2;
          k1 += 2 * m2;
          xr = a[j1];
          xi = a[j1 + 1];
          yr = a[k1];
          yi = a[k1 + 1];
          a[j1] = yr;
          a[j1 + 1] = yi;
          a[k1] = xr;
          a[k1 + 1] = xi;
          j1 += m2;
          k1 -= m2;
          xr = a[j1];
          xi = a[j1 + 1];
          yr = a[k1];
          yi = a[k1 + 1];
          a[j1] = yr;
          a[j1 + 1] = yi;
          a[k1] = xr;
          a[k1 + 1] = xi;
          j1 += m2;
          k1 += 2 * m2;
          xr = a[j1];
          xi = a[j1 + 1];
          yr = a[k1];
          yi = a[k1 + 1];
          a[j1] = yr;
          a[j1 + 1] = yi;
          a[k1] = xr;
          a[k1 + 1] = xi;
        }
        j1 = 2 * k + m2 + ip[ipP + k];
        k1 = j1 + m2;
        xr = a[j1];
        xi = a[j1 + 1];
        yr = a[k1];
        yi = a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
      }
    } else {
      for (k = 1; k < m; k++) {
        for (j = 0; j < k; j++) {
          j1 = 2 * j + ip[ipP + k];
          k1 = 2 * k + ip[ipP + j];
          xr = a[j1];
          xi = a[j1 + 1];
          yr = a[k1];
          yi = a[k1 + 1];
          a[j1] = yr;
          a[j1 + 1] = yi;
          a[k1] = xr;
          a[k1 + 1] = xi;
          j1 += m2;
          k1 += m2;
          xr = a[j1];
          xi = a[j1 + 1];
          yr = a[k1];
          yi = a[k1 + 1];
          a[j1] = yr;
          a[j1 + 1] = yi;
          a[k1] = xr;
          a[k1 + 1] = xi;
        }
      }
    }
  }

  /**
   * 3rd
   *
   * @see #cftbsub(int, double[], int[], int, int, double[])
   */
  private final void bitrv2conj(int n, int[] ip, int ipP, double[] a) {
    int j, j1, k, k1, l, m, m2;
    double xr, xi, yr, yi;

    ip[ipP + 0] = 0;
    l = n;
    m = 1;
    while ((m << 3) < l) {
      l >>= 1;
      for (j = 0; j < m; j++) {
        ip[ipP + m + j] = ip[ipP + j] + l;
      }
      m <<= 1;
    }
    m2 = 2 * m;
    if ((m << 3) == l) {
      for (k = 0; k < m; k++) {
        for (j = 0; j < k; j++) {
          j1 = 2 * j + ip[ipP + k];
          k1 = 2 * k + ip[ipP + j];
          xr = a[j1];
          xi = -a[j1 + 1];
          yr = a[k1];
          yi = -a[k1 + 1];
          a[j1] = yr;
          a[j1 + 1] = yi;
          a[k1] = xr;
          a[k1 + 1] = xi;
          j1 += m2;
          k1 += 2 * m2;
          xr = a[j1];
          xi = -a[j1 + 1];
          yr = a[k1];
          yi = -a[k1 + 1];
          a[j1] = yr;
          a[j1 + 1] = yi;
          a[k1] = xr;
          a[k1 + 1] = xi;
          j1 += m2;
          k1 -= m2;
          xr = a[j1];
          xi = -a[j1 + 1];
          yr = a[k1];
          yi = -a[k1 + 1];
          a[j1] = yr;
          a[j1 + 1] = yi;
          a[k1] = xr;
          a[k1 + 1] = xi;
          j1 += m2;
          k1 += 2 * m2;
          xr = a[j1];
          xi = -a[j1 + 1];
          yr = a[k1];
          yi = -a[k1 + 1];
          a[j1] = yr;
          a[j1 + 1] = yi;
          a[k1] = xr;
          a[k1 + 1] = xi;
        }
        k1 = 2 * k + ip[ipP + k];
        a[k1 + 1] = -a[k1 + 1];
        j1 = k1 + m2;
        k1 = j1 + m2;
        xr = a[j1];
        xi = -a[j1 + 1];
        yr = a[k1];
        yi = -a[k1 + 1];
        a[j1] = yr;
        a[j1 + 1] = yi;
        a[k1] = xr;
        a[k1 + 1] = xi;
        k1 += m2;
        a[k1 + 1] = -a[k1 + 1];
      }
    } else {
      a[1] = -a[1];
      a[m2 + 1] = -a[m2 + 1];
      for (k = 1; k < m; k++) {
        for (j = 0; j < k; j++) {
          j1 = 2 * j + ip[ipP + k];
          k1 = 2 * k + ip[ipP + j];
          xr = a[j1];
          xi = -a[j1 + 1];
          yr = a[k1];
          yi = -a[k1 + 1];
          a[j1] = yr;
          a[j1 + 1] = yi;
          a[k1] = xr;
          a[k1 + 1] = xi;
          j1 += m2;
          k1 += m2;
          xr = a[j1];
          xi = -a[j1 + 1];
          yr = a[k1];
          yi = -a[k1 + 1];
          a[j1] = yr;
          a[j1 + 1] = yi;
          a[k1] = xr;
          a[k1 + 1] = xi;
        }
        k1 = 2 * k + ip[ipP + k];
        a[k1 + 1] = -a[k1 + 1];
        a[k1 + m2 + 1] = -a[k1 + m2 + 1];
      }
    }
  }

  /**
   * 3rd
   *
   * @see #cftfsub(int, double[], int[], int, int, double[])
   */
  private void bitrv216(double[] a) {
    double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x7r, x7i, x8r, x8i, x10r, x10i, x11r,
        x11i, x12r, x12i, x13r, x13i, x14r, x14i;

    x1r = a[2];
    x1i = a[3];
    x2r = a[4];
    x2i = a[5];
    x3r = a[6];
    x3i = a[7];
    x4r = a[8];
    x4i = a[9];
    x5r = a[10];
    x5i = a[11];
    x7r = a[14];
    x7i = a[15];
    x8r = a[16];
    x8i = a[17];
    x10r = a[20];
    x10i = a[21];
    x11r = a[22];
    x11i = a[23];
    x12r = a[24];
    x12i = a[25];
    x13r = a[26];
    x13i = a[27];
    x14r = a[28];
    x14i = a[29];
    a[2] = x8r;
    a[3] = x8i;
    a[4] = x4r;
    a[5] = x4i;
    a[6] = x12r;
    a[7] = x12i;
    a[8] = x2r;
    a[9] = x2i;
    a[10] = x10r;
    a[11] = x10i;
    a[14] = x14r;
    a[15] = x14i;
    a[16] = x1r;
    a[17] = x1i;
    a[20] = x5r;
    a[21] = x5i;
    a[22] = x13r;
    a[23] = x13i;
    a[24] = x3r;
    a[25] = x3i;
    a[26] = x11r;
    a[27] = x11i;
    a[28] = x7r;
    a[29] = x7i;
  }

  /**
   * 3rd
   *
   * @see #cftbsub(int, double[], int[], int, int, double[])
   */
  private void bitrv216neg(double[] a) {
    double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x6r, x6i, x7r, x7i, x8r, x8i, x9r, x9i,
        x10r, x10i, x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i, x15r, x15i;

    x1r = a[2];
    x1i = a[3];
    x2r = a[4];
    x2i = a[5];
    x3r = a[6];
    x3i = a[7];
    x4r = a[8];
    x4i = a[9];
    x5r = a[10];
    x5i = a[11];
    x6r = a[12];
    x6i = a[13];
    x7r = a[14];
    x7i = a[15];
    x8r = a[16];
    x8i = a[17];
    x9r = a[18];
    x9i = a[19];
    x10r = a[20];
    x10i = a[21];
    x11r = a[22];
    x11i = a[23];
    x12r = a[24];
    x12i = a[25];
    x13r = a[26];
    x13i = a[27];
    x14r = a[28];
    x14i = a[29];
    x15r = a[30];
    x15i = a[31];
    a[2] = x15r;
    a[3] = x15i;
    a[4] = x7r;
    a[5] = x7i;
    a[6] = x11r;
    a[7] = x11i;
    a[8] = x3r;
    a[9] = x3i;
    a[10] = x13r;
    a[11] = x13i;
    a[12] = x5r;
    a[13] = x5i;
    a[14] = x9r;
    a[15] = x9i;
    a[16] = x1r;
    a[17] = x1i;
    a[18] = x14r;
    a[19] = x14i;
    a[20] = x6r;
    a[21] = x6i;
    a[22] = x10r;
    a[23] = x10i;
    a[24] = x2r;
    a[25] = x2i;
    a[26] = x12r;
    a[27] = x12i;
    a[28] = x4r;
    a[29] = x4i;
    a[30] = x8r;
    a[31] = x8i;
  }

  /**
   * 3rd
   *
   * @see #cftfsub(int, double[], int[], int, int, double[])
   */
  private void bitrv208(double[] a) {
    double x1r, x1i, x3r, x3i, x4r, x4i, x6r, x6i;

    x1r = a[2];
    x1i = a[3];
    x3r = a[6];
    x3i = a[7];
    x4r = a[8];
    x4i = a[9];
    x6r = a[12];
    x6i = a[13];
    a[2] = x4r;
    a[3] = x4i;
    a[6] = x6r;
    a[7] = x6i;
    a[8] = x1r;
    a[9] = x1i;
    a[12] = x3r;
    a[13] = x3i;
  }

  /**
   * 3rd
   *
   * @see #cftbsub(int, double[], int[], int, int, double[])
   */
  private void bitrv208neg(double[] a) {
    double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x6r, x6i, x7r, x7i;

    x1r = a[2];
    x1i = a[3];
    x2r = a[4];
    x2i = a[5];
    x3r = a[6];
    x3i = a[7];
    x4r = a[8];
    x4i = a[9];
    x5r = a[10];
    x5i = a[11];
    x6r = a[12];
    x6i = a[13];
    x7r = a[14];
    x7i = a[15];
    a[2] = x7r;
    a[3] = x7i;
    a[4] = x3r;
    a[5] = x3i;
    a[6] = x5r;
    a[7] = x5i;
    a[8] = x1r;
    a[9] = x1i;
    a[10] = x6r;
    a[11] = x6i;
    a[12] = x2r;
    a[13] = x2i;
    a[14] = x4r;
    a[15] = x4i;
  }

  /**
   * 3rd
   *
   * @see #cftfsub(int, double[], int[], int, int, double[])
   */
  private void cftf1st(int n, double[] a, double[] w, int wP) {
    int j, j0, j1, j2, j3, k, m, mh;
    double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;

    mh = n >> 3;
    m = 2 * mh;
    j1 = m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[0] + a[j2];
    x0i = a[1] + a[j2 + 1];
    x1r = a[0] - a[j2];
    x1i = a[1] - a[j2 + 1];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    a[0] = x0r + x2r;
    a[1] = x0i + x2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i - x2i;
    a[j2] = x1r - x3i;
    a[j2 + 1] = x1i + x3r;
    a[j3] = x1r + x3i;
    a[j3 + 1] = x1i - x3r;
    wn4r = w[wP + 1];
    csc1 = w[wP + 2];
    csc3 = w[wP + 3];
    wd1r = 1;
    wd1i = 0;
    wd3r = 1;
    wd3i = 0;
    k = 0;
    for (j = 2; j < mh - 2; j += 4) {
      k += 4;
      wk1r = csc1 * (wd1r + w[wP + k]);
      wk1i = csc1 * (wd1i + w[wP + k + 1]);
      wk3r = csc3 * (wd3r + w[wP + k + 2]);
      wk3i = csc3 * (wd3i - w[wP + k + 3]);
      wd1r = w[wP + k];
      wd1i = w[wP + k + 1];
      wd3r = w[wP + k + 2];
      wd3i = -w[wP + k + 3];
      j1 = j + m;
      j2 = j1 + m;
      j3 = j2 + m;
      x0r = a[j] + a[j2];
      x0i = a[j + 1] + a[j2 + 1];
      x1r = a[j] - a[j2];
      x1i = a[j + 1] - a[j2 + 1];
      y0r = a[j + 2] + a[j2 + 2];
      y0i = a[j + 3] + a[j2 + 3];
      y1r = a[j + 2] - a[j2 + 2];
      y1i = a[j + 3] - a[j2 + 3];
      x2r = a[j1] + a[j3];
      x2i = a[j1 + 1] + a[j3 + 1];
      x3r = a[j1] - a[j3];
      x3i = a[j1 + 1] - a[j3 + 1];
      y2r = a[j1 + 2] + a[j3 + 2];
      y2i = a[j1 + 3] + a[j3 + 3];
      y3r = a[j1 + 2] - a[j3 + 2];
      y3i = a[j1 + 3] - a[j3 + 3];
      a[j] = x0r + x2r;
      a[j + 1] = x0i + x2i;
      a[j + 2] = y0r + y2r;
      a[j + 3] = y0i + y2i;
      a[j1] = x0r - x2r;
      a[j1 + 1] = x0i - x2i;
      a[j1 + 2] = y0r - y2r;
      a[j1 + 3] = y0i - y2i;
      x0r = x1r - x3i;
      x0i = x1i + x3r;
      a[j2] = wk1r * x0r - wk1i * x0i;
      a[j2 + 1] = wk1r * x0i + wk1i * x0r;
      x0r = y1r - y3i;
      x0i = y1i + y3r;
      a[j2 + 2] = wd1r * x0r - wd1i * x0i;
      a[j2 + 3] = wd1r * x0i + wd1i * x0r;
      x0r = x1r + x3i;
      x0i = x1i - x3r;
      a[j3] = wk3r * x0r + wk3i * x0i;
      a[j3 + 1] = wk3r * x0i - wk3i * x0r;
      x0r = y1r + y3i;
      x0i = y1i - y3r;
      a[j3 + 2] = wd3r * x0r + wd3i * x0i;
      a[j3 + 3] = wd3r * x0i - wd3i * x0r;
      j0 = m - j;
      j1 = j0 + m;
      j2 = j1 + m;
      j3 = j2 + m;
      x0r = a[j0] + a[j2];
      x0i = a[j0 + 1] + a[j2 + 1];
      x1r = a[j0] - a[j2];
      x1i = a[j0 + 1] - a[j2 + 1];
      y0r = a[j0 - 2] + a[j2 - 2];
      y0i = a[j0 - 1] + a[j2 - 1];
      y1r = a[j0 - 2] - a[j2 - 2];
      y1i = a[j0 - 1] - a[j2 - 1];
      x2r = a[j1] + a[j3];
      x2i = a[j1 + 1] + a[j3 + 1];
      x3r = a[j1] - a[j3];
      x3i = a[j1 + 1] - a[j3 + 1];
      y2r = a[j1 - 2] + a[j3 - 2];
      y2i = a[j1 - 1] + a[j3 - 1];
      y3r = a[j1 - 2] - a[j3 - 2];
      y3i = a[j1 - 1] - a[j3 - 1];
      a[j0] = x0r + x2r;
      a[j0 + 1] = x0i + x2i;
      a[j0 - 2] = y0r + y2r;
      a[j0 - 1] = y0i + y2i;
      a[j1] = x0r - x2r;
      a[j1 + 1] = x0i - x2i;
      a[j1 - 2] = y0r - y2r;
      a[j1 - 1] = y0i - y2i;
      x0r = x1r - x3i;
      x0i = x1i + x3r;
      a[j2] = wk1i * x0r - wk1r * x0i;
      a[j2 + 1] = wk1i * x0i + wk1r * x0r;
      x0r = y1r - y3i;
      x0i = y1i + y3r;
      a[j2 - 2] = wd1i * x0r - wd1r * x0i;
      a[j2 - 1] = wd1i * x0i + wd1r * x0r;
      x0r = x1r + x3i;
      x0i = x1i - x3r;
      a[j3] = wk3i * x0r + wk3r * x0i;
      a[j3 + 1] = wk3i * x0i - wk3r * x0r;
      x0r = y1r + y3i;
      x0i = y1i - y3r;
      a[j3 - 2] = wd3i * x0r + wd3r * x0i;
      a[j3 - 1] = wd3i * x0i - wd3r * x0r;
    }
    wk1r = csc1 * (wd1r + wn4r);
    wk1i = csc1 * (wd1i + wn4r);
    wk3r = csc3 * (wd3r - wn4r);
    wk3i = csc3 * (wd3i - wn4r);
    j0 = mh;
    j1 = j0 + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[j0 - 2] + a[j2 - 2];
    x0i = a[j0 - 1] + a[j2 - 1];
    x1r = a[j0 - 2] - a[j2 - 2];
    x1i = a[j0 - 1] - a[j2 - 1];
    x2r = a[j1 - 2] + a[j3 - 2];
    x2i = a[j1 - 1] + a[j3 - 1];
    x3r = a[j1 - 2] - a[j3 - 2];
    x3i = a[j1 - 1] - a[j3 - 1];
    a[j0 - 2] = x0r + x2r;
    a[j0 - 1] = x0i + x2i;
    a[j1 - 2] = x0r - x2r;
    a[j1 - 1] = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[j2 - 2] = wk1r * x0r - wk1i * x0i;
    a[j2 - 1] = wk1r * x0i + wk1i * x0r;
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    a[j3 - 2] = wk3r * x0r + wk3i * x0i;
    a[j3 - 1] = wk3r * x0i - wk3i * x0r;
    x0r = a[j0] + a[j2];
    x0i = a[j0 + 1] + a[j2 + 1];
    x1r = a[j0] - a[j2];
    x1i = a[j0 + 1] - a[j2 + 1];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    a[j0] = x0r + x2r;
    a[j0 + 1] = x0i + x2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[j2] = wn4r * (x0r - x0i);
    a[j2 + 1] = wn4r * (x0i + x0r);
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    a[j3] = -wn4r * (x0r + x0i);
    a[j3 + 1] = -wn4r * (x0i - x0r);
    x0r = a[j0 + 2] + a[j2 + 2];
    x0i = a[j0 + 3] + a[j2 + 3];
    x1r = a[j0 + 2] - a[j2 + 2];
    x1i = a[j0 + 3] - a[j2 + 3];
    x2r = a[j1 + 2] + a[j3 + 2];
    x2i = a[j1 + 3] + a[j3 + 3];
    x3r = a[j1 + 2] - a[j3 + 2];
    x3i = a[j1 + 3] - a[j3 + 3];
    a[j0 + 2] = x0r + x2r;
    a[j0 + 3] = x0i + x2i;
    a[j1 + 2] = x0r - x2r;
    a[j1 + 3] = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[j2 + 2] = wk1i * x0r - wk1r * x0i;
    a[j2 + 3] = wk1i * x0i + wk1r * x0r;
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    a[j3 + 2] = wk3i * x0r + wk3r * x0i;
    a[j3 + 3] = wk3i * x0i - wk3r * x0r;
  }

  /**
   * 3rd
   *
   * @see #cftbsub(int, double[], int[], int, int, double[])
   */
  private final void cftb1st(int n, double[] a, double[] w, int wP) {
    int j, j0, j1, j2, j3, k, m, mh;
    double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;

    mh = n >> 3;
    m = 2 * mh;
    j1 = m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[0] + a[j2];
    x0i = -a[1] - a[j2 + 1];
    x1r = a[0] - a[j2];
    x1i = -a[1] + a[j2 + 1];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    a[0] = x0r + x2r;
    a[1] = x0i - x2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i + x2i;
    a[j2] = x1r + x3i;
    a[j2 + 1] = x1i + x3r;
    a[j3] = x1r - x3i;
    a[j3 + 1] = x1i - x3r;
    wn4r = w[wP + 1];
    csc1 = w[wP + 2];
    csc3 = w[wP + 3];
    wd1r = 1;
    wd1i = 0;
    wd3r = 1;
    wd3i = 0;
    k = 0;
    for (j = 2; j < mh - 2; j += 4) {
      k += 4;
      wk1r = csc1 * (wd1r + w[wP + k]);
      wk1i = csc1 * (wd1i + w[wP + k + 1]);
      wk3r = csc3 * (wd3r + w[wP + k + 2]);
      wk3i = csc3 * (wd3i - w[wP + k + 3]);
      wd1r = w[wP + k];
      wd1i = w[wP + k + 1];
      wd3r = w[wP + k + 2];
      wd3i = -w[wP + k + 3];
      j1 = j + m;
      j2 = j1 + m;
      j3 = j2 + m;
      x0r = a[j] + a[j2];
      x0i = -a[j + 1] - a[j2 + 1];
      x1r = a[j] - a[j2];
      x1i = -a[j + 1] + a[j2 + 1];
      y0r = a[j + 2] + a[j2 + 2];
      y0i = -a[j + 3] - a[j2 + 3];
      y1r = a[j + 2] - a[j2 + 2];
      y1i = -a[j + 3] + a[j2 + 3];
      x2r = a[j1] + a[j3];
      x2i = a[j1 + 1] + a[j3 + 1];
      x3r = a[j1] - a[j3];
      x3i = a[j1 + 1] - a[j3 + 1];
      y2r = a[j1 + 2] + a[j3 + 2];
      y2i = a[j1 + 3] + a[j3 + 3];
      y3r = a[j1 + 2] - a[j3 + 2];
      y3i = a[j1 + 3] - a[j3 + 3];
      a[j] = x0r + x2r;
      a[j + 1] = x0i - x2i;
      a[j + 2] = y0r + y2r;
      a[j + 3] = y0i - y2i;
      a[j1] = x0r - x2r;
      a[j1 + 1] = x0i + x2i;
      a[j1 + 2] = y0r - y2r;
      a[j1 + 3] = y0i + y2i;
      x0r = x1r + x3i;
      x0i = x1i + x3r;
      a[j2] = wk1r * x0r - wk1i * x0i;
      a[j2 + 1] = wk1r * x0i + wk1i * x0r;
      x0r = y1r + y3i;
      x0i = y1i + y3r;
      a[j2 + 2] = wd1r * x0r - wd1i * x0i;
      a[j2 + 3] = wd1r * x0i + wd1i * x0r;
      x0r = x1r - x3i;
      x0i = x1i - x3r;
      a[j3] = wk3r * x0r + wk3i * x0i;
      a[j3 + 1] = wk3r * x0i - wk3i * x0r;
      x0r = y1r - y3i;
      x0i = y1i - y3r;
      a[j3 + 2] = wd3r * x0r + wd3i * x0i;
      a[j3 + 3] = wd3r * x0i - wd3i * x0r;
      j0 = m - j;
      j1 = j0 + m;
      j2 = j1 + m;
      j3 = j2 + m;
      x0r = a[j0] + a[j2];
      x0i = -a[j0 + 1] - a[j2 + 1];
      x1r = a[j0] - a[j2];
      x1i = -a[j0 + 1] + a[j2 + 1];
      y0r = a[j0 - 2] + a[j2 - 2];
      y0i = -a[j0 - 1] - a[j2 - 1];
      y1r = a[j0 - 2] - a[j2 - 2];
      y1i = -a[j0 - 1] + a[j2 - 1];
      x2r = a[j1] + a[j3];
      x2i = a[j1 + 1] + a[j3 + 1];
      x3r = a[j1] - a[j3];
      x3i = a[j1 + 1] - a[j3 + 1];
      y2r = a[j1 - 2] + a[j3 - 2];
      y2i = a[j1 - 1] + a[j3 - 1];
      y3r = a[j1 - 2] - a[j3 - 2];
      y3i = a[j1 - 1] - a[j3 - 1];
      a[j0] = x0r + x2r;
      a[j0 + 1] = x0i - x2i;
      a[j0 - 2] = y0r + y2r;
      a[j0 - 1] = y0i - y2i;
      a[j1] = x0r - x2r;
      a[j1 + 1] = x0i + x2i;
      a[j1 - 2] = y0r - y2r;
      a[j1 - 1] = y0i + y2i;
      x0r = x1r + x3i;
      x0i = x1i + x3r;
      a[j2] = wk1i * x0r - wk1r * x0i;
      a[j2 + 1] = wk1i * x0i + wk1r * x0r;
      x0r = y1r + y3i;
      x0i = y1i + y3r;
      a[j2 - 2] = wd1i * x0r - wd1r * x0i;
      a[j2 - 1] = wd1i * x0i + wd1r * x0r;
      x0r = x1r - x3i;
      x0i = x1i - x3r;
      a[j3] = wk3i * x0r + wk3r * x0i;
      a[j3 + 1] = wk3i * x0i - wk3r * x0r;
      x0r = y1r - y3i;
      x0i = y1i - y3r;
      a[j3 - 2] = wd3i * x0r + wd3r * x0i;
      a[j3 - 1] = wd3i * x0i - wd3r * x0r;
    }
    wk1r = csc1 * (wd1r + wn4r);
    wk1i = csc1 * (wd1i + wn4r);
    wk3r = csc3 * (wd3r - wn4r);
    wk3i = csc3 * (wd3i - wn4r);
    j0 = mh;
    j1 = j0 + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[j0 - 2] + a[j2 - 2];
    x0i = -a[j0 - 1] - a[j2 - 1];
    x1r = a[j0 - 2] - a[j2 - 2];
    x1i = -a[j0 - 1] + a[j2 - 1];
    x2r = a[j1 - 2] + a[j3 - 2];
    x2i = a[j1 - 1] + a[j3 - 1];
    x3r = a[j1 - 2] - a[j3 - 2];
    x3i = a[j1 - 1] - a[j3 - 1];
    a[j0 - 2] = x0r + x2r;
    a[j0 - 1] = x0i - x2i;
    a[j1 - 2] = x0r - x2r;
    a[j1 - 1] = x0i + x2i;
    x0r = x1r + x3i;
    x0i = x1i + x3r;
    a[j2 - 2] = wk1r * x0r - wk1i * x0i;
    a[j2 - 1] = wk1r * x0i + wk1i * x0r;
    x0r = x1r - x3i;
    x0i = x1i - x3r;
    a[j3 - 2] = wk3r * x0r + wk3i * x0i;
    a[j3 - 1] = wk3r * x0i - wk3i * x0r;
    x0r = a[j0] + a[j2];
    x0i = -a[j0 + 1] - a[j2 + 1];
    x1r = a[j0] - a[j2];
    x1i = -a[j0 + 1] + a[j2 + 1];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    a[j0] = x0r + x2r;
    a[j0 + 1] = x0i - x2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i + x2i;
    x0r = x1r + x3i;
    x0i = x1i + x3r;
    a[j2] = wn4r * (x0r - x0i);
    a[j2 + 1] = wn4r * (x0i + x0r);
    x0r = x1r - x3i;
    x0i = x1i - x3r;
    a[j3] = -wn4r * (x0r + x0i);
    a[j3 + 1] = -wn4r * (x0i - x0r);
    x0r = a[j0 + 2] + a[j2 + 2];
    x0i = -a[j0 + 3] - a[j2 + 3];
    x1r = a[j0 + 2] - a[j2 + 2];
    x1i = -a[j0 + 3] + a[j2 + 3];
    x2r = a[j1 + 2] + a[j3 + 2];
    x2i = a[j1 + 3] + a[j3 + 3];
    x3r = a[j1 + 2] - a[j3 + 2];
    x3i = a[j1 + 3] - a[j3 + 3];
    a[j0 + 2] = x0r + x2r;
    a[j0 + 3] = x0i - x2i;
    a[j1 + 2] = x0r - x2r;
    a[j1 + 3] = x0i + x2i;
    x0r = x1r + x3i;
    x0i = x1i + x3r;
    a[j2 + 2] = wk1i * x0r - wk1r * x0i;
    a[j2 + 3] = wk1i * x0i + wk1r * x0r;
    x0r = x1r - x3i;
    x0i = x1i - x3r;
    a[j3 + 2] = wk3i * x0r + wk3r * x0i;
    a[j3 + 3] = wk3i * x0i - wk3r * x0r;
  }

  /** */
  private void cftrec1(int n, double[] a, int aP, int nw, double[] w) {
    int m;

    m = n >> 2;
    cftmdl1(n, a, aP, w, nw - 2 * m);
    if (n > CDFT_RECURSIVE_N) {
      cftrec1(m, a, aP, nw, w);
      cftrec2(m, a, aP + m, nw, w);
      cftrec1(m, a, aP + 2 * m, nw, w);
      cftrec1(m, a, aP + 3 * m, nw, w);
    } else {
      cftexp1(n, a, aP, nw, w);
    }
  }

  /** */
  private void cftrec2(int n, double[] a, int aP, int nw, double[] w) {
    int m;

    m = n >> 2;
    cftmdl2(n, a, aP, w, nw - n);
    if (n > CDFT_RECURSIVE_N) {
      cftrec1(m, a, aP, nw, w);
      cftrec2(m, a, aP + m, nw, w);
      cftrec1(m, a, aP + 2 * m, nw, w);
      cftrec2(m, a, aP + 3 * m, nw, w);
    } else {
      cftexp2(n, a, aP, nw, w);
    }
  }

  /** */
  private void cftexp1(int n, double[] a, int aP, int nw, double[] w) {
    int j, k, l;

    l = n >> 2;
    while (l > 128) {
      for (k = l; k < n; k <<= 2) {
        for (j = k - l; j < n; j += 4 * k) {
          cftmdl1(l, a, aP + j, w, nw - (l >> 1));
          cftmdl2(l, a, aP + k + j, w, nw - l);
          cftmdl1(l, a, aP + 2 * k + j, w, nw - (l >> 1));
        }
      }
      cftmdl1(l, a, aP + n - l, w, nw - (l >> 1));
      l >>= 2;
    }
    for (k = l; k < n; k <<= 2) {
      for (j = k - l; j < n; j += 4 * k) {
        cftmdl1(l, a, aP + j, w, nw - (l >> 1));
        cftfx41(l, a, aP + j, nw, w);
        cftmdl2(l, a, aP + k + j, w, nw - l);
        cftfx42(l, a, aP + k + j, nw, w);
        cftmdl1(l, a, aP + 2 * k + j, w, nw - (l >> 1));
        cftfx41(l, a, aP + 2 * k + j, nw, w);
      }
    }
    cftmdl1(l, a, aP + n - l, w, nw - (l >> 1));
    cftfx41(l, a, aP + n - l, nw, w);
  }

  /** */
  private void cftexp2(int n, double[] a, int aP, int nw, double[] w) {
    int j, k, l, m;

    m = n >> 1;
    l = n >> 2;
    while (l > 128) {
      for (k = l; k < m; k <<= 2) {
        for (j = k - l; j < m; j += 2 * k) {
          cftmdl1(l, a, aP + j, w, nw - (l >> 1));
          cftmdl1(l, a, aP + m + j, w, nw - (l >> 1));
        }
        for (j = 2 * k - l; j < m; j += 4 * k) {
          cftmdl2(l, a, aP + j, w, nw - l);
          cftmdl2(l, a, aP + m + j, w, nw - l);
        }
      }
      l >>= 2;
    }
    for (k = l; k < m; k <<= 2) {
      for (j = k - l; j < m; j += 2 * k) {
        cftmdl1(l, a, aP + j, w, nw - (l >> 1));
        cftfx41(l, a, aP + j, nw, w);
        cftmdl1(l, a, aP + m + j, w, nw - (l >> 1));
        cftfx41(l, a, aP + m + j, nw, w);
      }
      for (j = 2 * k - l; j < m; j += 4 * k) {
        cftmdl2(l, a, aP + j, w, nw - l);
        cftfx42(l, a, aP + j, nw, w);
        cftmdl2(l, a, aP + m + j, w, nw - l);
        cftfx42(l, a, aP + m + j, nw, w);
      }
    }
  }

  /** */
  private final void cftmdl1(int n, double[] a, int aP, double[] w, int wP) {
    int j, j0, j1, j2, j3, k, m, mh;
    double wn4r, wk1r, wk1i, wk3r, wk3i;
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

    mh = n >> 3;
    m = 2 * mh;
    j1 = m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[aP + 0] + a[aP + j2];
    x0i = a[aP + 1] + a[aP + j2 + 1];
    x1r = a[aP + 0] - a[aP + j2];
    x1i = a[aP + 1] - a[aP + j2 + 1];
    x2r = a[aP + j1] + a[aP + j3];
    x2i = a[aP + j1 + 1] + a[aP + j3 + 1];
    x3r = a[aP + j1] - a[aP + j3];
    x3i = a[aP + j1 + 1] - a[aP + j3 + 1];
    a[aP + 0] = x0r + x2r;
    a[aP + 1] = x0i + x2i;
    a[aP + j1] = x0r - x2r;
    a[aP + j1 + 1] = x0i - x2i;
    a[aP + j2] = x1r - x3i;
    a[aP + j2 + 1] = x1i + x3r;
    a[aP + j3] = x1r + x3i;
    a[aP + j3 + 1] = x1i - x3r;
    wn4r = w[wP + 1];
    k = 0;
    for (j = 2; j < mh; j += 2) {
      k += 4;
      wk1r = w[wP + k];
      wk1i = w[wP + k + 1];
      wk3r = w[wP + k + 2];
      wk3i = -w[wP + k + 3];
      j1 = j + m;
      j2 = j1 + m;
      j3 = j2 + m;
      x0r = a[aP + j] + a[aP + j2];
      x0i = a[aP + j + 1] + a[aP + j2 + 1];
      x1r = a[aP + j] - a[aP + j2];
      x1i = a[aP + j + 1] - a[aP + j2 + 1];
      x2r = a[aP + j1] + a[aP + j3];
      x2i = a[aP + j1 + 1] + a[aP + j3 + 1];
      x3r = a[aP + j1] - a[aP + j3];
      x3i = a[aP + j1 + 1] - a[aP + j3 + 1];
      a[aP + j] = x0r + x2r;
      a[aP + j + 1] = x0i + x2i;
      a[aP + j1] = x0r - x2r;
      a[aP + j1 + 1] = x0i - x2i;
      x0r = x1r - x3i;
      x0i = x1i + x3r;
      a[aP + j2] = wk1r * x0r - wk1i * x0i;
      a[aP + j2 + 1] = wk1r * x0i + wk1i * x0r;
      x0r = x1r + x3i;
      x0i = x1i - x3r;
      a[aP + j3] = wk3r * x0r + wk3i * x0i;
      a[aP + j3 + 1] = wk3r * x0i - wk3i * x0r;
      j0 = m - j;
      j1 = j0 + m;
      j2 = j1 + m;
      j3 = j2 + m;
      x0r = a[aP + j0] + a[aP + j2];
      x0i = a[aP + j0 + 1] + a[aP + j2 + 1];
      x1r = a[aP + j0] - a[aP + j2];
      x1i = a[aP + j0 + 1] - a[aP + j2 + 1];
      x2r = a[aP + j1] + a[aP + j3];
      x2i = a[aP + j1 + 1] + a[aP + j3 + 1];
      x3r = a[aP + j1] - a[aP + j3];
      x3i = a[aP + j1 + 1] - a[aP + j3 + 1];
      a[aP + j0] = x0r + x2r;
      a[aP + j0 + 1] = x0i + x2i;
      a[aP + j1] = x0r - x2r;
      a[aP + j1 + 1] = x0i - x2i;
      x0r = x1r - x3i;
      x0i = x1i + x3r;
      a[aP + j2] = wk1i * x0r - wk1r * x0i;
      a[aP + j2 + 1] = wk1i * x0i + wk1r * x0r;
      x0r = x1r + x3i;
      x0i = x1i - x3r;
      a[aP + j3] = wk3i * x0r + wk3r * x0i;
      a[aP + j3 + 1] = wk3i * x0i - wk3r * x0r;
    }
    j0 = mh;
    j1 = j0 + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[aP + j0] + a[aP + j2];
    x0i = a[aP + j0 + 1] + a[aP + j2 + 1];
    x1r = a[aP + j0] - a[aP + j2];
    x1i = a[aP + j0 + 1] - a[aP + j2 + 1];
    x2r = a[aP + j1] + a[aP + j3];
    x2i = a[aP + j1 + 1] + a[aP + j3 + 1];
    x3r = a[aP + j1] - a[aP + j3];
    x3i = a[aP + j1 + 1] - a[aP + j3 + 1];
    a[aP + j0] = x0r + x2r;
    a[aP + j0 + 1] = x0i + x2i;
    a[aP + j1] = x0r - x2r;
    a[aP + j1 + 1] = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[aP + j2] = wn4r * (x0r - x0i);
    a[aP + j2 + 1] = wn4r * (x0i + x0r);
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    a[aP + j3] = -wn4r * (x0r + x0i);
    a[aP + j3 + 1] = -wn4r * (x0i - x0r);
  }

  /** */
  private final void cftmdl2(int n, double[] a, int aP, double[] w, int wP) {
    int j, j0, j1, j2, j3, k, kr, m, mh;
    double wn4r, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i;

    mh = n >> 3;
    m = 2 * mh;
    wn4r = w[wP + 1];
    j1 = m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[aP + 0] - a[aP + j2 + 1];
    x0i = a[aP + 1] + a[aP + j2];
    x1r = a[aP + 0] + a[aP + j2 + 1];
    x1i = a[aP + 1] - a[aP + j2];
    x2r = a[aP + j1] - a[aP + j3 + 1];
    x2i = a[aP + j1 + 1] + a[aP + j3];
    x3r = a[aP + j1] + a[aP + j3 + 1];
    x3i = a[aP + j1 + 1] - a[aP + j3];
    y0r = wn4r * (x2r - x2i);
    y0i = wn4r * (x2i + x2r);
    a[aP + 0] = x0r + y0r;
    a[aP + 1] = x0i + y0i;
    a[aP + j1] = x0r - y0r;
    a[aP + j1 + 1] = x0i - y0i;
    y0r = wn4r * (x3r - x3i);
    y0i = wn4r * (x3i + x3r);
    a[aP + j2] = x1r - y0i;
    a[aP + j2 + 1] = x1i + y0r;
    a[aP + j3] = x1r + y0i;
    a[aP + j3 + 1] = x1i - y0r;
    k = 0;
    kr = 2 * m;
    for (j = 2; j < mh; j += 2) {
      k += 4;
      wk1r = w[wP + k];
      wk1i = w[wP + k + 1];
      wk3r = w[wP + k + 2];
      wk3i = -w[wP + k + 3];
      kr -= 4;
      wd1i = w[wP + kr];
      wd1r = w[wP + kr + 1];
      wd3i = w[wP + kr + 2];
      wd3r = -w[wP + kr + 3];
      j1 = j + m;
      j2 = j1 + m;
      j3 = j2 + m;
      x0r = a[aP + j] - a[aP + j2 + 1];
      x0i = a[aP + j + 1] + a[aP + j2];
      x1r = a[aP + j] + a[aP + j2 + 1];
      x1i = a[aP + j + 1] - a[aP + j2];
      x2r = a[aP + j1] - a[aP + j3 + 1];
      x2i = a[aP + j1 + 1] + a[aP + j3];
      x3r = a[aP + j1] + a[aP + j3 + 1];
      x3i = a[aP + j1 + 1] - a[aP + j3];
      y0r = wk1r * x0r - wk1i * x0i;
      y0i = wk1r * x0i + wk1i * x0r;
      y2r = wd1r * x2r - wd1i * x2i;
      y2i = wd1r * x2i + wd1i * x2r;
      a[aP + j] = y0r + y2r;
      a[aP + j + 1] = y0i + y2i;
      a[aP + j1] = y0r - y2r;
      a[aP + j1 + 1] = y0i - y2i;
      y0r = wk3r * x1r + wk3i * x1i;
      y0i = wk3r * x1i - wk3i * x1r;
      y2r = wd3r * x3r + wd3i * x3i;
      y2i = wd3r * x3i - wd3i * x3r;
      a[aP + j2] = y0r + y2r;
      a[aP + j2 + 1] = y0i + y2i;
      a[aP + j3] = y0r - y2r;
      a[aP + j3 + 1] = y0i - y2i;
      j0 = m - j;
      j1 = j0 + m;
      j2 = j1 + m;
      j3 = j2 + m;
      x0r = a[aP + j0] - a[aP + j2 + 1];
      x0i = a[aP + j0 + 1] + a[aP + j2];
      x1r = a[aP + j0] + a[aP + j2 + 1];
      x1i = a[aP + j0 + 1] - a[aP + j2];
      x2r = a[aP + j1] - a[aP + j3 + 1];
      x2i = a[aP + j1 + 1] + a[aP + j3];
      x3r = a[aP + j1] + a[aP + j3 + 1];
      x3i = a[aP + j1 + 1] - a[aP + j3];
      y0r = wd1i * x0r - wd1r * x0i;
      y0i = wd1i * x0i + wd1r * x0r;
      y2r = wk1i * x2r - wk1r * x2i;
      y2i = wk1i * x2i + wk1r * x2r;
      a[aP + j0] = y0r + y2r;
      a[aP + j0 + 1] = y0i + y2i;
      a[aP + j1] = y0r - y2r;
      a[aP + j1 + 1] = y0i - y2i;
      y0r = wd3i * x1r + wd3r * x1i;
      y0i = wd3i * x1i - wd3r * x1r;
      y2r = wk3i * x3r + wk3r * x3i;
      y2i = wk3i * x3i - wk3r * x3r;
      a[aP + j2] = y0r + y2r;
      a[aP + j2 + 1] = y0i + y2i;
      a[aP + j3] = y0r - y2r;
      a[aP + j3 + 1] = y0i - y2i;
    }
    wk1r = w[wP + m];
    wk1i = w[wP + m + 1];
    j0 = mh;
    j1 = j0 + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[aP + j0] - a[aP + j2 + 1];
    x0i = a[aP + j0 + 1] + a[aP + j2];
    x1r = a[aP + j0] + a[aP + j2 + 1];
    x1i = a[aP + j0 + 1] - a[aP + j2];
    x2r = a[aP + j1] - a[aP + j3 + 1];
    x2i = a[aP + j1 + 1] + a[aP + j3];
    x3r = a[aP + j1] + a[aP + j3 + 1];
    x3i = a[aP + j1 + 1] - a[aP + j3];
    y0r = wk1r * x0r - wk1i * x0i;
    y0i = wk1r * x0i + wk1i * x0r;
    y2r = wk1i * x2r - wk1r * x2i;
    y2i = wk1i * x2i + wk1r * x2r;
    a[aP + j0] = y0r + y2r;
    a[aP + j0 + 1] = y0i + y2i;
    a[aP + j1] = y0r - y2r;
    a[aP + j1 + 1] = y0i - y2i;
    y0r = wk1i * x1r - wk1r * x1i;
    y0i = wk1i * x1i + wk1r * x1r;
    y2r = wk1r * x3r - wk1i * x3i;
    y2i = wk1r * x3i + wk1i * x3r;
    a[aP + j2] = y0r - y2r;
    a[aP + j2 + 1] = y0i - y2i;
    a[aP + j3] = y0r + y2r;
    a[aP + j3 + 1] = y0i + y2i;
  }

  /** */
  private void cftfx41(int n, double[] a, int aP, int nw, double[] w) {
    if (n == 128) {
      cftf161(a, aP, w, nw - 8);
      cftf162(a, aP + 32, w, nw - 32);
      cftf161(a, aP + 64, w, nw - 8);
      cftf161(a, aP + 96, w, nw - 8);
    } else {
      cftf081(a, aP, w, nw - 16);
      cftf082(a, aP + 16, w, nw - 16);
      cftf081(a, aP + 32, w, nw - 16);
      cftf081(a, aP + 48, w, nw - 16);
    }
  }

  /** */
  private void cftfx42(int n, double[] a, int aP, int nw, double[] w) {
    if (n == 128) {
      cftf161(a, aP, w, nw - 8);
      cftf162(a, aP + 32, w, nw - 32);
      cftf161(a, aP + 64, w, nw - 8);
      cftf162(a, aP + 96, w, nw - 32);
    } else {
      cftf081(a, aP, w, nw - 16);
      cftf082(a, aP + 16, w, nw - 16);
      cftf081(a, aP + 32, w, nw - 16);
      cftf082(a, aP + 48, w, nw - 16);
    }
  }

  /** */
  private void cftf161(double[] a, int aP, double[] w, int wP) {
    double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i,
        y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i, y8r, y8i, y9r, y9i, y10r, y10i, y11r,
        y11i, y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;

    wn4r = w[wP + 1];
    wk1i = wn4r * w[wP + 2];
    wk1r = wk1i + w[wP + 2];
    x0r = a[aP + 0] + a[aP + 16];
    x0i = a[aP + 1] + a[aP + 17];
    x1r = a[aP + 0] - a[aP + 16];
    x1i = a[aP + 1] - a[aP + 17];
    x2r = a[aP + 8] + a[aP + 24];
    x2i = a[aP + 9] + a[aP + 25];
    x3r = a[aP + 8] - a[aP + 24];
    x3i = a[aP + 9] - a[aP + 25];
    y0r = x0r + x2r;
    y0i = x0i + x2i;
    y4r = x0r - x2r;
    y4i = x0i - x2i;
    y8r = x1r - x3i;
    y8i = x1i + x3r;
    y12r = x1r + x3i;
    y12i = x1i - x3r;
    x0r = a[aP + 2] + a[aP + 18];
    x0i = a[aP + 3] + a[aP + 19];
    x1r = a[aP + 2] - a[aP + 18];
    x1i = a[aP + 3] - a[aP + 19];
    x2r = a[aP + 10] + a[aP + 26];
    x2i = a[aP + 11] + a[aP + 27];
    x3r = a[aP + 10] - a[aP + 26];
    x3i = a[aP + 11] - a[aP + 27];
    y1r = x0r + x2r;
    y1i = x0i + x2i;
    y5r = x0r - x2r;
    y5i = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    y9r = wk1r * x0r - wk1i * x0i;
    y9i = wk1r * x0i + wk1i * x0r;
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    y13r = wk1i * x0r - wk1r * x0i;
    y13i = wk1i * x0i + wk1r * x0r;
    x0r = a[aP + 4] + a[aP + 20];
    x0i = a[aP + 5] + a[aP + 21];
    x1r = a[aP + 4] - a[aP + 20];
    x1i = a[aP + 5] - a[aP + 21];
    x2r = a[aP + 12] + a[aP + 28];
    x2i = a[aP + 13] + a[aP + 29];
    x3r = a[aP + 12] - a[aP + 28];
    x3i = a[aP + 13] - a[aP + 29];
    y2r = x0r + x2r;
    y2i = x0i + x2i;
    y6r = x0r - x2r;
    y6i = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    y10r = wn4r * (x0r - x0i);
    y10i = wn4r * (x0i + x0r);
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    y14r = wn4r * (x0r + x0i);
    y14i = wn4r * (x0i - x0r);
    x0r = a[aP + 6] + a[aP + 22];
    x0i = a[aP + 7] + a[aP + 23];
    x1r = a[aP + 6] - a[aP + 22];
    x1i = a[aP + 7] - a[aP + 23];
    x2r = a[aP + 14] + a[aP + 30];
    x2i = a[aP + 15] + a[aP + 31];
    x3r = a[aP + 14] - a[aP + 30];
    x3i = a[aP + 15] - a[aP + 31];
    y3r = x0r + x2r;
    y3i = x0i + x2i;
    y7r = x0r - x2r;
    y7i = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    y11r = wk1i * x0r - wk1r * x0i;
    y11i = wk1i * x0i + wk1r * x0r;
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    y15r = wk1r * x0r - wk1i * x0i;
    y15i = wk1r * x0i + wk1i * x0r;
    x0r = y12r - y14r;
    x0i = y12i - y14i;
    x1r = y12r + y14r;
    x1i = y12i + y14i;
    x2r = y13r - y15r;
    x2i = y13i - y15i;
    x3r = y13r + y15r;
    x3i = y13i + y15i;
    a[aP + 24] = x0r + x2r;
    a[aP + 25] = x0i + x2i;
    a[aP + 26] = x0r - x2r;
    a[aP + 27] = x0i - x2i;
    a[aP + 28] = x1r - x3i;
    a[aP + 29] = x1i + x3r;
    a[aP + 30] = x1r + x3i;
    a[aP + 31] = x1i - x3r;
    x0r = y8r + y10r;
    x0i = y8i + y10i;
    x1r = y8r - y10r;
    x1i = y8i - y10i;
    x2r = y9r + y11r;
    x2i = y9i + y11i;
    x3r = y9r - y11r;
    x3i = y9i - y11i;
    a[aP + 16] = x0r + x2r;
    a[aP + 17] = x0i + x2i;
    a[aP + 18] = x0r - x2r;
    a[aP + 19] = x0i - x2i;
    a[aP + 20] = x1r - x3i;
    a[aP + 21] = x1i + x3r;
    a[aP + 22] = x1r + x3i;
    a[aP + 23] = x1i - x3r;
    x0r = y5r - y7i;
    x0i = y5i + y7r;
    x2r = wn4r * (x0r - x0i);
    x2i = wn4r * (x0i + x0r);
    x0r = y5r + y7i;
    x0i = y5i - y7r;
    x3r = wn4r * (x0r - x0i);
    x3i = wn4r * (x0i + x0r);
    x0r = y4r - y6i;
    x0i = y4i + y6r;
    x1r = y4r + y6i;
    x1i = y4i - y6r;
    a[aP + 8] = x0r + x2r;
    a[aP + 9] = x0i + x2i;
    a[aP + 10] = x0r - x2r;
    a[aP + 11] = x0i - x2i;
    a[aP + 12] = x1r - x3i;
    a[aP + 13] = x1i + x3r;
    a[aP + 14] = x1r + x3i;
    a[aP + 15] = x1i - x3r;
    x0r = y0r + y2r;
    x0i = y0i + y2i;
    x1r = y0r - y2r;
    x1i = y0i - y2i;
    x2r = y1r + y3r;
    x2i = y1i + y3i;
    x3r = y1r - y3r;
    x3i = y1i - y3i;
    a[aP + 0] = x0r + x2r;
    a[aP + 1] = x0i + x2i;
    a[aP + 2] = x0r - x2r;
    a[aP + 3] = x0i - x2i;
    a[aP + 4] = x1r - x3i;
    a[aP + 5] = x1i + x3r;
    a[aP + 6] = x1r + x3i;
    a[aP + 7] = x1i - x3r;
  }

  /** */
  private void cftf162(double[] a, int aP, double[] w, int wP) {
    double wn4r, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i, x0r, x0i, x1r, x1i, x2r, x2i, y0r, y0i, y1r,
        y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i, y8r, y8i, y9r, y9i, y10r,
        y10i, y11r, y11i, y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;

    wn4r = w[wP + 1];
    wk1r = w[wP + 4];
    wk1i = w[wP + 5];
    wk3r = w[wP + 6];
    wk3i = w[wP + 7];
    wk2r = w[wP + 8];
    wk2i = w[wP + 9];
    x1r = a[aP + 0] - a[aP + 17];
    x1i = a[aP + 1] + a[aP + 16];
    x0r = a[aP + 8] - a[aP + 25];
    x0i = a[aP + 9] + a[aP + 24];
    x2r = wn4r * (x0r - x0i);
    x2i = wn4r * (x0i + x0r);
    y0r = x1r + x2r;
    y0i = x1i + x2i;
    y4r = x1r - x2r;
    y4i = x1i - x2i;
    x1r = a[aP + 0] + a[aP + 17];
    x1i = a[aP + 1] - a[aP + 16];
    x0r = a[aP + 8] + a[aP + 25];
    x0i = a[aP + 9] - a[aP + 24];
    x2r = wn4r * (x0r - x0i);
    x2i = wn4r * (x0i + x0r);
    y8r = x1r - x2i;
    y8i = x1i + x2r;
    y12r = x1r + x2i;
    y12i = x1i - x2r;
    x0r = a[aP + 2] - a[aP + 19];
    x0i = a[aP + 3] + a[aP + 18];
    x1r = wk1r * x0r - wk1i * x0i;
    x1i = wk1r * x0i + wk1i * x0r;
    x0r = a[aP + 10] - a[aP + 27];
    x0i = a[aP + 11] + a[aP + 26];
    x2r = wk3i * x0r - wk3r * x0i;
    x2i = wk3i * x0i + wk3r * x0r;
    y1r = x1r + x2r;
    y1i = x1i + x2i;
    y5r = x1r - x2r;
    y5i = x1i - x2i;
    x0r = a[aP + 2] + a[aP + 19];
    x0i = a[aP + 3] - a[aP + 18];
    x1r = wk3r * x0r - wk3i * x0i;
    x1i = wk3r * x0i + wk3i * x0r;
    x0r = a[aP + 10] + a[aP + 27];
    x0i = a[aP + 11] - a[aP + 26];
    x2r = wk1r * x0r + wk1i * x0i;
    x2i = wk1r * x0i - wk1i * x0r;
    y9r = x1r - x2r;
    y9i = x1i - x2i;
    y13r = x1r + x2r;
    y13i = x1i + x2i;
    x0r = a[aP + 4] - a[aP + 21];
    x0i = a[aP + 5] + a[aP + 20];
    x1r = wk2r * x0r - wk2i * x0i;
    x1i = wk2r * x0i + wk2i * x0r;
    x0r = a[aP + 12] - a[aP + 29];
    x0i = a[aP + 13] + a[aP + 28];
    x2r = wk2i * x0r - wk2r * x0i;
    x2i = wk2i * x0i + wk2r * x0r;
    y2r = x1r + x2r;
    y2i = x1i + x2i;
    y6r = x1r - x2r;
    y6i = x1i - x2i;
    x0r = a[aP + 4] + a[aP + 21];
    x0i = a[aP + 5] - a[aP + 20];
    x1r = wk2i * x0r - wk2r * x0i;
    x1i = wk2i * x0i + wk2r * x0r;
    x0r = a[aP + 12] + a[aP + 29];
    x0i = a[aP + 13] - a[aP + 28];
    x2r = wk2r * x0r - wk2i * x0i;
    x2i = wk2r * x0i + wk2i * x0r;
    y10r = x1r - x2r;
    y10i = x1i - x2i;
    y14r = x1r + x2r;
    y14i = x1i + x2i;
    x0r = a[aP + 6] - a[aP + 23];
    x0i = a[aP + 7] + a[aP + 22];
    x1r = wk3r * x0r - wk3i * x0i;
    x1i = wk3r * x0i + wk3i * x0r;
    x0r = a[aP + 14] - a[aP + 31];
    x0i = a[aP + 15] + a[aP + 30];
    x2r = wk1i * x0r - wk1r * x0i;
    x2i = wk1i * x0i + wk1r * x0r;
    y3r = x1r + x2r;
    y3i = x1i + x2i;
    y7r = x1r - x2r;
    y7i = x1i - x2i;
    x0r = a[aP + 6] + a[aP + 23];
    x0i = a[aP + 7] - a[aP + 22];
    x1r = wk1i * x0r + wk1r * x0i;
    x1i = wk1i * x0i - wk1r * x0r;
    x0r = a[aP + 14] + a[aP + 31];
    x0i = a[aP + 15] - a[aP + 30];
    x2r = wk3i * x0r - wk3r * x0i;
    x2i = wk3i * x0i + wk3r * x0r;
    y11r = x1r + x2r;
    y11i = x1i + x2i;
    y15r = x1r - x2r;
    y15i = x1i - x2i;
    x1r = y0r + y2r;
    x1i = y0i + y2i;
    x2r = y1r + y3r;
    x2i = y1i + y3i;
    a[aP + 0] = x1r + x2r;
    a[aP + 1] = x1i + x2i;
    a[aP + 2] = x1r - x2r;
    a[aP + 3] = x1i - x2i;
    x1r = y0r - y2r;
    x1i = y0i - y2i;
    x2r = y1r - y3r;
    x2i = y1i - y3i;
    a[aP + 4] = x1r - x2i;
    a[aP + 5] = x1i + x2r;
    a[aP + 6] = x1r + x2i;
    a[aP + 7] = x1i - x2r;
    x1r = y4r - y6i;
    x1i = y4i + y6r;
    x0r = y5r - y7i;
    x0i = y5i + y7r;
    x2r = wn4r * (x0r - x0i);
    x2i = wn4r * (x0i + x0r);
    a[aP + 8] = x1r + x2r;
    a[aP + 9] = x1i + x2i;
    a[aP + 10] = x1r - x2r;
    a[aP + 11] = x1i - x2i;
    x1r = y4r + y6i;
    x1i = y4i - y6r;
    x0r = y5r + y7i;
    x0i = y5i - y7r;
    x2r = wn4r * (x0r - x0i);
    x2i = wn4r * (x0i + x0r);
    a[aP + 12] = x1r - x2i;
    a[aP + 13] = x1i + x2r;
    a[aP + 14] = x1r + x2i;
    a[aP + 15] = x1i - x2r;
    x1r = y8r + y10r;
    x1i = y8i + y10i;
    x2r = y9r - y11r;
    x2i = y9i - y11i;
    a[aP + 16] = x1r + x2r;
    a[aP + 17] = x1i + x2i;
    a[aP + 18] = x1r - x2r;
    a[aP + 19] = x1i - x2i;
    x1r = y8r - y10r;
    x1i = y8i - y10i;
    x2r = y9r + y11r;
    x2i = y9i + y11i;
    a[aP + 20] = x1r - x2i;
    a[aP + 21] = x1i + x2r;
    a[aP + 22] = x1r + x2i;
    a[aP + 23] = x1i - x2r;
    x1r = y12r - y14i;
    x1i = y12i + y14r;
    x0r = y13r + y15i;
    x0i = y13i - y15r;
    x2r = wn4r * (x0r - x0i);
    x2i = wn4r * (x0i + x0r);
    a[aP + 24] = x1r + x2r;
    a[aP + 25] = x1i + x2i;
    a[aP + 26] = x1r - x2r;
    a[aP + 27] = x1i - x2i;
    x1r = y12r + y14i;
    x1i = y12i - y14r;
    x0r = y13r - y15i;
    x0i = y13i + y15r;
    x2r = wn4r * (x0r - x0i);
    x2i = wn4r * (x0i + x0r);
    a[aP + 28] = x1r - x2i;
    a[aP + 29] = x1i + x2r;
    a[aP + 30] = x1r + x2i;
    a[aP + 31] = x1i - x2r;
  }

  /** */
  private void cftf081(double[] a, int aP, double[] w, int wP) {
    double wn4r, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
        y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;

    wn4r = w[wP + 1];
    x0r = a[aP + 0] + a[aP + 8];
    x0i = a[aP + 1] + a[aP + 9];
    x1r = a[aP + 0] - a[aP + 8];
    x1i = a[aP + 1] - a[aP + 9];
    x2r = a[aP + 4] + a[aP + 12];
    x2i = a[aP + 5] + a[aP + 13];
    x3r = a[aP + 4] - a[aP + 12];
    x3i = a[aP + 5] - a[aP + 13];
    y0r = x0r + x2r;
    y0i = x0i + x2i;
    y2r = x0r - x2r;
    y2i = x0i - x2i;
    y1r = x1r - x3i;
    y1i = x1i + x3r;
    y3r = x1r + x3i;
    y3i = x1i - x3r;
    x0r = a[aP + 2] + a[aP + 10];
    x0i = a[aP + 3] + a[aP + 11];
    x1r = a[aP + 2] - a[aP + 10];
    x1i = a[aP + 3] - a[aP + 11];
    x2r = a[aP + 6] + a[aP + 14];
    x2i = a[aP + 7] + a[aP + 15];
    x3r = a[aP + 6] - a[aP + 14];
    x3i = a[aP + 7] - a[aP + 15];
    y4r = x0r + x2r;
    y4i = x0i + x2i;
    y6r = x0r - x2r;
    y6i = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    x2r = x1r + x3i;
    x2i = x1i - x3r;
    y5r = wn4r * (x0r - x0i);
    y5i = wn4r * (x0r + x0i);
    y7r = wn4r * (x2r - x2i);
    y7i = wn4r * (x2r + x2i);
    a[aP + 8] = y1r + y5r;
    a[aP + 9] = y1i + y5i;
    a[aP + 10] = y1r - y5r;
    a[aP + 11] = y1i - y5i;
    a[aP + 12] = y3r - y7i;
    a[aP + 13] = y3i + y7r;
    a[aP + 14] = y3r + y7i;
    a[aP + 15] = y3i - y7r;
    a[aP + 0] = y0r + y4r;
    a[aP + 1] = y0i + y4i;
    a[aP + 2] = y0r - y4r;
    a[aP + 3] = y0i - y4i;
    a[aP + 4] = y2r - y6i;
    a[aP + 5] = y2i + y6r;
    a[aP + 6] = y2r + y6i;
    a[aP + 7] = y2i - y6r;
  }

  /** */
  private void cftf082(double[] a, int aP, double[] w, int wP) {
    double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i,
        y5r, y5i, y6r, y6i, y7r, y7i;

    wn4r = w[wP + 1];
    wk1r = w[wP + 4];
    wk1i = w[wP + 5];
    y0r = a[aP + 0] - a[aP + 9];
    y0i = a[aP + 1] + a[aP + 8];
    y1r = a[aP + 0] + a[aP + 9];
    y1i = a[aP + 1] - a[aP + 8];
    x0r = a[aP + 4] - a[aP + 13];
    x0i = a[aP + 5] + a[aP + 12];
    y2r = wn4r * (x0r - x0i);
    y2i = wn4r * (x0i + x0r);
    x0r = a[aP + 4] + a[aP + 13];
    x0i = a[aP + 5] - a[aP + 12];
    y3r = wn4r * (x0r - x0i);
    y3i = wn4r * (x0i + x0r);
    x0r = a[aP + 2] - a[aP + 11];
    x0i = a[aP + 3] + a[aP + 10];
    y4r = wk1r * x0r - wk1i * x0i;
    y4i = wk1r * x0i + wk1i * x0r;
    x0r = a[aP + 2] + a[aP + 11];
    x0i = a[aP + 3] - a[aP + 10];
    y5r = wk1i * x0r - wk1r * x0i;
    y5i = wk1i * x0i + wk1r * x0r;
    x0r = a[aP + 6] - a[aP + 15];
    x0i = a[aP + 7] + a[aP + 14];
    y6r = wk1i * x0r - wk1r * x0i;
    y6i = wk1i * x0i + wk1r * x0r;
    x0r = a[aP + 6] + a[aP + 15];
    x0i = a[aP + 7] - a[aP + 14];
    y7r = wk1r * x0r - wk1i * x0i;
    y7i = wk1r * x0i + wk1i * x0r;
    x0r = y0r + y2r;
    x0i = y0i + y2i;
    x1r = y4r + y6r;
    x1i = y4i + y6i;
    a[aP + 0] = x0r + x1r;
    a[aP + 1] = x0i + x1i;
    a[aP + 2] = x0r - x1r;
    a[aP + 3] = x0i - x1i;
    x0r = y0r - y2r;
    x0i = y0i - y2i;
    x1r = y4r - y6r;
    x1i = y4i - y6i;
    a[aP + 4] = x0r - x1i;
    a[aP + 5] = x0i + x1r;
    a[aP + 6] = x0r + x1i;
    a[aP + 7] = x0i - x1r;
    x0r = y1r - y3i;
    x0i = y1i + y3r;
    x1r = y5r - y7r;
    x1i = y5i - y7i;
    a[aP + 8] = x0r + x1r;
    a[aP + 9] = x0i + x1i;
    a[aP + 10] = x0r - x1r;
    a[aP + 11] = x0i - x1i;
    x0r = y1r + y3i;
    x0i = y1i - y3r;
    x1r = y5r + y7r;
    x1i = y5i + y7i;
    a[aP + 12] = x0r - x1i;
    a[aP + 13] = x0i + x1r;
    a[aP + 14] = x0r + x1i;
    a[aP + 15] = x0i - x1r;
  }

  /**
   * 3rd
   * when n = 8.
   *
   * @see #cftfsub(int, double[], int[], int, int, double[])
   */
  private void cftf040(double[] a) {
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

    x0r = a[0] + a[4];
    x0i = a[1] + a[5];
    x1r = a[0] - a[4];
    x1i = a[1] - a[5];
    x2r = a[2] + a[6];
    x2i = a[3] + a[7];
    x3r = a[2] - a[6];
    x3i = a[3] - a[7];
    a[0] = x0r + x2r;
    a[1] = x0i + x2i;
    a[4] = x0r - x2r;
    a[5] = x0i - x2i;
    a[2] = x1r - x3i;
    a[3] = x1i + x3r;
    a[6] = x1r + x3i;
    a[7] = x1i - x3r;
  }

  /**
   * 3rd
   * when n = 8.
   *
   * @see #cftbsub(int, double[], int[], int, int, double[])
   */
  private void cftb040(double[] a) {
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

    x0r = a[0] + a[4];
    x0i = a[1] + a[5];
    x1r = a[0] - a[4];
    x1i = a[1] - a[5];
    x2r = a[2] + a[6];
    x2i = a[3] + a[7];
    x3r = a[2] - a[6];
    x3i = a[3] - a[7];
    a[0] = x0r + x2r;
    a[1] = x0i + x2i;
    a[4] = x0r - x2r;
    a[5] = x0i - x2i;
    a[2] = x1r + x3i;
    a[3] = x1i - x3r;
    a[6] = x1r - x3i;
    a[7] = x1i + x3r;
  }

  /**
   * 3rd
   * when n = 4.
   *
   * @see #cftbsub(int, double[], int[], int, int, double[])
   * @see #cftfsub(int, double[], int[], int, int, double[])
   */
  private void cftx020(double[] a) {
    double x0r, x0i;

    x0r = a[0] - a[2];
    x0i = a[1] - a[3];
    a[0] += a[2];
    a[1] += a[3];
    a[2] = x0r;
    a[3] = x0i;
  }

  /**
   * 2nd
   *
   * @see #rdft(int, int, double[], int[], double[])
   * @see #ddct(int, int, double[], int[], double[])
   * @see #ddst(int, int, double[], int[], double[])
   * @see #dfst(int, double[], double[], int[], double[])
   * @see #dfct(int, double[], double[], int[], double[])
   */
  private void rftfsub(int n, double[] a, int nc, double[] c, int cP) {
    int j, k, kk, ks, m;
    double wkr, wki, xr, xi, yr, yi;

    m = n >> 1;
    ks = 2 * nc / m;
    kk = 0;
    for (j = 2; j < m; j += 2) {
      k = n - j;
      kk += ks;
      wkr = 0.5 - c[cP + nc - kk];
      wki = c[cP + kk];
      xr = a[j] - a[k];
      xi = a[j + 1] + a[k + 1];
      yr = wkr * xr - wki * xi;
      yi = wkr * xi + wki * xr;
      a[j] -= yr;
      a[j + 1] -= yi;
      a[k] += yr;
      a[k + 1] -= yi;
    }
  }

  /**
   * 2nd
   *
   * @see #rdft(int, int, double[], int[], double[])
   * @see #ddct(int, int, double[], int[], double[])
   * @see #ddst(int, int, double[], int[], double[])
   */
  private void rftbsub(int n, double[] a, int nc, double[] c, int cP) {
    int j, k, kk, ks, m;
    double wkr, wki, xr, xi, yr, yi;

    m = n >> 1;
    ks = 2 * nc / m;
    kk = 0;
    for (j = 2; j < m; j += 2) {
      k = n - j;
      kk += ks;
      wkr = 0.5 - c[cP + nc - kk];
      wki = c[cP + kk];
      xr = a[j] - a[k];
      xi = a[j + 1] + a[k + 1];
      yr = wkr * xr + wki * xi;
      yi = wkr * xi - wki * xr;
      a[j] -= yr;
      a[j + 1] -= yi;
      a[k] += yr;
      a[k + 1] -= yi;
    }
  }

  /**
   * 2nd
   *
   * @see #ddct(int, int, double[], int[], double[])
   * @see #dfct(int, double[], double[], int[], double[])
   */
  private void dctsub(int n, double[] a, int nc, double[] c, int cP) {
    int j, k, kk, ks, m;
    double wkr, wki, xr;

    m = n >> 1;
    ks = nc / n;
    kk = 0;
    for (j = 1; j < m; j++) {
      k = n - j;
      kk += ks;
      wkr = c[cP + kk] - c[cP + nc - kk];
      wki = c[cP + kk] + c[cP + nc - kk];
      xr = wki * a[j] - wkr * a[k];
      a[j] = wkr * a[j] + wki * a[k];
      a[k] = xr;
    }
    a[m] *= c[cP + 0];
  }

  /**
   * 2nd
   *
   * @see #ddst(int, int, double[], int[], double[])
   * @see #dfst(int, double[], double[], int[], double[])
   */
  private void dstsub(int n, double[] a, int nc, double[] c, int cP) {
    int j, k, kk, ks, m;
    double wkr, wki, xr;

    m = n >> 1;
    ks = nc / n;
    kk = 0;
    for (j = 1; j < m; j++) {
      k = n - j;
      kk += ks;
      wkr = c[cP + kk] - c[cP + nc - kk];
      wki = c[cP + kk] + c[cP + nc - kk];
      xr = wki * a[k] - wkr * a[j];
      a[k] = wkr * a[k] + wki * a[j];
      a[j] = xr;
    }
    a[m] *= c[cP + 0];
  }
}

/* */
